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x = 11, y = 41

Step-by-step explanation:

The angles m < (4x + 6)° and m < (6x - 16)° are alternate interior angles that do not have a common vertex, and lie on the alternate sides of the transversal. Alternate interior angles also have the same measure.

Additionally, the exterior angle, m < (y + 9)° and the interior angle, m < (4x + 5)° are corresponding angles that have the same measure.

To solve for the values of x we can establish the following equality statement:

m < (4x + 6)° =  m < (6x - 16)°

4x + 6 = 6x - 16  

Subtract 4x from both sides:

4x - 4x + 6 = 6x - 4x - 16  

6 = 2x - 16

Add 16 to both sides:

16 + 6 = 2x - 16 + 16

22 = 2x

Divide both sides by 2:

22/2 = 2x/2

11 = x

Now that we have the value of x = 11, we can substitute this value into the following equation to solve for y:

4x + 6 = y + 9

4(11) + 6 = y + 9

44 + 6 = y + 9

50 = y + 9

Subtract 9 from both sides:

50 - 9 = y + 9 - 9

41 = y

Double-check whether we have the correct value for x:

m < (4x + 6)° =  m < (6x - 16)°

4(11) + 6 = 6(11) - 16

50 = 50 (True statement. This means that we have the correct value for x).

Do the same thing for the following to verify whether we have the correct value for y:

m < (4x + 6)° = m < (y + 9)°

4(11) + 6 = 41 + 9

50 = 50 (True statement).

Therefore, the correct answers are: x = 11, y = 41.

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